Scale Drawings

2026 What You Need to Know (Syllabus Objectives)

By the end of this topic, you should be able to:

  1. Draw and interpret scale drawings
  2. Use and interpret three-figure bearings
  3. Understand that bearings are measured clockwise from north (000° to 360°), and know how to find the bearing of A from B when given the bearing of B from A
  4. Understand the terms north, east, south and west (e.g., point D is due east of point C)
  5. Use a ruler for all straight edges in your drawings

Section 1: Understanding Scale

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What is a Scale?

A scale is a ratio that shows the relationship between a distance on a drawing or map and the actual distance in real life.

For example, if a map has a scale of 1:50,000, this means:

  • 1 cm on the map = 50,000 cm in real life
  • 1 inch on the map = 50,000 inches in real life
  • The ratio works for any unit, as long as you use the same unit on both sides

Scales are used because real-life objects and distances are often too large to draw at their actual size. A scale allows us to make accurate smaller versions.

How to Write a Scale

Scales are written in two main ways:

Method 1: As a ratio

  • Written as 1:n (where n is a number)
  • Example: 1:100 means 1 unit on the drawing = 100 units in real life

Method 2: As a statement

  • Written with units
  • Example: 1 cm = 5 km means 1 centimetre on the map represents 5 kilometres in real life

Important Scale Rule

The scale ratio 1:n has no units because both sides use the same unit. You can use any unit (cm, m, km, inches, etc.), but whatever unit you measure with on the drawing, the real-life distance will be in that same unit multiplied by n.

Section 2: Working with Scale Drawings

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Converting a Scale to Useful Units

Often, you will need to convert a scale into units that make sense for your problem.

Example: If the scale is 1:150,000 and you want to know how many kilometres 1 cm on the map represents:

Step 1: Start with the ratio in centimetres

  • 1 cm on map = 150,000 cm in real life

Step 2: Convert to metres

  • 150,000 cm ÷ 100 = 1,500 m

Step 3: Convert to kilometres

  • 1,500 m ÷ 1,000 = 1.5 km

Result: The scale can be written as 1 cm = 1.5 km

Finding Actual Distances from a Scale Drawing

To find the real-life distance when you have a measurement from a drawing:

Step 1: Measure the distance on the drawing using a ruler (in cm or mm)

Step 2: Multiply by the scale factor to get the actual distance in the same units

Step 3: Convert to appropriate units (m, km, etc.) if needed

Example:

  • Scale: 1:12,000
  • Distance on map: 1.7 cm
  • Actual distance: 1.7 × 12,000 = 20,400 cm = 204 m

Finding Drawing Distances from Actual Distances

To find how long to draw something on a scale drawing when you know the real-life distance:

Step 1: Make sure the real-life distance and the scale are in the same units (usually convert the real distance to cm)

Step 2: Divide the actual distance by the scale factor

Step 3: This gives you the length to draw on your drawing

Example:

  • Scale: 1 cm = 5 km
  • Actual distance: 20 km
  • Drawing distance: 20 ÷ 5 = 4 cm

Drawing Scale Diagrams Accurately

When asked to draw a scale drawing, you must:

  • Use a sharp pencil for accuracy
  • Use a ruler for all straight edges (this is required in exams)
  • Measure carefully and accurately
  • Label your drawing with measurements and the scale used
  • Show any construction marks (like arcs from a compass) if requested

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